Strategic interaction and NFNE. The case of co2 concentration

After the first formulation of optimal control problems in the middle of the 20th century, model predictive control (MPC) and nonlinear model predictive control (NMPC) gradually became popular methods in both science and industry. Considering the advantages of NMPC as a practical method to solve dynamic decision problems numerically, this method could attract more attention in economics too. Later, in order to model strategic interactions between different policymakers, NMPC was extended to the NMPC feedback Nash equilibrium (NFNE). With focusing on these novel and practical techniques, the aims of this thesis are considered as follows. First, taking into account the privileges of mentioned techniques (NMPC and NFNE) such as repetitive solution of an optimal control problem in a receding horizon fashion and considering the time horizon, we use them in an environmental topic and assess the effects of different regimes on the climate change. Second, referring to the time horizon as a significant factor in these meth-ods, we evaluate the effect of “Different time horizons” on the results and finally, we extend the current NFNE method in order to have more accurate predictions, specifically where we face more than one state variable in our optimization problems. In this thesis, we consider a significant climate issue as global warming. Since using non-renewable energy and as its result CO2 concentration leads to the negative externalities and affects individual welfare, for evaluating the interactions between different policymakers, we use a canonical growth model augmented with damages in the household’s welfare function. We assess the CO2 concentration level when players operate under different regimes, in this thesis by different regimes, we refer to the cooperative and non-cooperative policies and we consider the period from 2019 to 2100. We start considering one common state variable as CO2 con-centration and one control variable as using non-renewable energy. Our result shows a big difference in the CO2 concentration level in the cooperative and non-cooperative situation. Although, with cooperation between independent policymakers we can reach a lower level of externality but, still it is not the best emission pathway. However, if policymakers find it difficult (e.g., for political reasons) to accept international binding agreements, and prefer to rely on their preferences for consuming non-renewal recourses instead of considering the global warming, the negative externalities and damaging effects may be quite severe. Moreover, along the line of Sims’s idea that agents often make decisions under in-formation constraint, we interpret the finite horizon as a measure of inattention or myopia. When we apply different time horizons for introducing the policymakers’ myopia, we observe that interestingly, less myopic policymakers anticipate much less CO2 concentration above the pre-industrial level. However, results state that also if we find a way to remove policy uncertainty or constraints and have a more precise prediction (i.e., longer time horizon), still the result will not be satisfying by the year 2100. Then, in our extended form of NFNE, we consider the transition from non-renewable to renewable energy as an important way to combat global warming. This transition can also be considered as an additional instrument in cooperative situations. Hence, we suppose two state variables. Along with CO2 concentration which is the common state variable, we take into account the capital stock to produce renewable energy. Also, we have two control variables as the extraction rate of fossil fuels and consumption. But, this extension in our model requires an extension in the method. So, we extend the current NFNE method and build two separate loops as two different games for optimization problems. These loops should be solved independently but simultaneously to find those fixed points that players have no incentive to change that at each point of time. Results show that despite having the renewable resources, since there is not a suitable cooperation between countries/policymakers, we cannot expect to have a transition from non-renewable to renewable resources. But interestingly, if policymakers accept a high degree of cooperation, we will reach really good results in CO2 concentration and eventually temperature.